3 Answers
3

Some mods, like mods regarding high-res textures, are single-player mods that do not affect the communication with the server, and can therefore be used irrespective of server configuration.

Other mods, like aircraft mods, require server support in order to work.

In general, the description of any given mod will list if it's compatible with vanilla servers, if it only takes effect in SSP, or if it requires a modded server.

Edit: In response to comments; one piece of clarification:

Some mods function somewhat more like exploits based on the fact that the server allows a certain amount of client-side processing of things like falling. Mods that function by misrepresenting the effects of gravity, for instance, can function without server support, at least until the communication protocol is changed to handle all movement server-side, assuming that ever happens.

Some mods, like the ability to fly, do affect communication with the server, yet don't require server support. (Tho servers now can kick people off who do use flying, if so configured.)
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dlras2Jul 21 '11 at 15:02

I've heard of the planes mod being used on a smp server by forcing all players to download it, did they also have to do some heavy configuring or what's the deal?
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Garet ClabornJul 21 '11 at 15:09

Yes you can, it's easy - download the mod, copy the classes to minecraft.jar, run Minecraft, then close Minecraft, open %appdata%/.minecraft and there will be a text document called single player commands or spc or something like that. Open that, at the very bottom of the txt file press enter and type: